Absence of blow-up in a fully parabolic chemotaxis system with weak singular sensitivity and logistic damping in dimension two
Year: 2025
Type: preprint
Abstract: It is shown in this paper that blow-up does not occur in the following chemotaxis system under homogeneous Neumann boundary conditions in a smooth, open, bounded domain Ω ⊂ R 2 : { u t = ∆ u − χ ∇ · ( u v k ∇ v ) + ru − µ u 2 , in Ω × ( 0 , T max ) , v t = ∆ v − αv + βu , in Ω × ( 0 , T max ) , where k ∈(0 , 1), and χ,r,µ,α,β are positive parameters. Known results have already established the same conclusion for the parabolic-elliptic case. Here, we complement these findings by extending the result to the fully parabolic case.
Author: Minh Le
Institution: Westlake University
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
OpenAlex ID: W4411370802